bbarrons,
At the risk of blatantly promoting some external company, I've used DynDNS services for several years. (I'm not in any way attached to them ... other than paying them for services.) They offer a very complete set up "auxiliary" services around anything DNS/domain related. Their DNS hosting has been great, their MX backups have never failed me, and their staff is quick to respond and knowledgeable.
I agree with phoenix, you need a proper MX backup. It won't cost you much, not compared to the hassle of trying to restore and download lost emails during an outage. Tell your employer to pony up $50/year, or whatever it costs.
